Quiz

I think Ment's solution is correct. I figured it out like this: One condemned person can identify the poison in two barrels. Give one person a taste from one barrel; if they die, the poison is in that barrel; if not, it's in the other. Two people in four barrels. The first drinks from the first barrel, the second from the second, both from the third, and neither from the fourth. Therefore, the third barrel is among eight. Four people in sixteen. Five people in thirty-two. Or, the number of barrels is 2ⁿ, where n is the number of condemned people. Therefore, the first time, we'll select 5 groups of 16 barrels each, and one condemned person will drink from each. If only one dies, the poison is definitely in one of those 16 barrels, and the remaining four are enough to figure out which one. That's 16 * 5 = 80 barrels. The number of combinations of five groups of two barrels each, with two prisoners drinking from all possible combinations, is 5!/(2!*3!) = 120/(2*6) = 10 groups of 8 barrels - 80 barrels. If two prisoners die, the remaining three are enough to identify the poison in the group of 8 barrels. The number of combinations of five groups of three barrels each, with four barrels in each, is 5!/(3!*2!) = 10 groups of 4 barrels - 40 barrels. If three die, the remaining two are enough to identify the poison in the four barrels. The number of combinations of five groups of four barrels each, with two barrels in each, is 5!/(4!*1!) = 5. In total, 5 * 2 = 10 barrels. If four die, even one is enough to identify the poison in the two barrels from which all four drank. In one of them, they will all drink the poison together. If they all die, the poison is in that barrel, which is one more barrel. So, let's calculate how many barrels we've already used: 80 + 80 + 40 + 10 + 1 = 211 barrels. If none of them die, the poison is in the remaining 29 barrels, and as shown above, five people can identify the poison in 32 barrels - let alone 29. So, the poison can be identified in a total of 211 + 32 = 243 barrels. Ment, you're the one who came up with the solution. You're great. I'll try to understand your solution again.